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A necessary geometric condition for the existence of certain homoclinic orbits

Published online by Cambridge University Press:  24 October 2008

J. F. Toland
J. F. Toland
Affiliation:
School of Mathematics, University of Bath, Bath BA2 7AY
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Extract

Throughout this brief note V denotes a fixed, smooth, real-valued function on such that there exists a bounded, open, strictly convex set C with (the boundary of C), V > 0 in C, V = 0 on and V′(0) = 0.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 100 , Issue 3 , November 1986 , pp. 591 - 594
Copyright
Copyright © Cambridge Philosophical Society 1986

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References

REFERENCES

[1]Toland, J. F., The existence of symmetric homoclinic orbits for systems of Euler—Lagrange equations. Proc. A.M.S. Symposium (Berkeley), (1983), (to appear).Google Scholar
[2]Hofer, H., and Toland, J. F., Homoclinic, heteroclinic and periodic solutions for indefinite Hamiltonian systems. Math. Ann. 268 (1984), 387–403.CrossRefGoogle Scholar
[3]Toland, J. F., Hamiltonian systems with a natural order structure. Nonlinear functional analysis and its applications (Reidel, 1986), 147–160.CrossRefGoogle Scholar